1) Fluid Reynolds number calculation
Where, v is the characteristic velocity of the flow field, in m/s; L is the characteristic length of the flow field, in m.
During the operation of high-speed spiral bevel gears, the surrounding air is stirred, and the Reynolds number of the flow field can reach 90000, so the internal air flow pattern is turbulent.
2) Fluid Mach number calculation
Where, a is the local sound velocity of the flow field, in m/s. The maximum velocity of fluid is close to the large end linear velocity of spiral bevel gear. The sound velocity is 340 m/s when the standard is taken. 0.3 Ma can be obtained, so the air inside the gearbox can be regarded as an incompressible fluid.
3) Reynolds mean equation
Because there is a nonlinear term (u ▽ u) in the momentum conservation equation, and the velocity has the dual role of control and feedback, there is no effective mathematical processing method to directly solve the N-S equation at present. The turbulence model equation is changed from the N-S equation to the Reynolds average equation that averages it.
Subtract Reynolds average equation from instantaneous control equation to obtain Reynolds pulsation equation:
N-S (Navier Stokes) equation, Reynolds mean equation and Reynolds pulsation equation together constitute the basic equation for studying turbulence.